Department of Mathematics

Department of Mathematics

Publications:

  • Generalized Fibonacci sequence and Analytical Properties, Vikram Mathematical Journal, Vol. 26, (2006), 131-144.
  • Standard Proof Techniques for Formulas of Fibonacci and Lucas Polynomials, Varahmihir Journal of Mathematical Sciences, Vol. 7, No. 2, (2007), 217-224.
  • Standard Proof Techniques for Generalized Fibonacci Sequence, Varahmihir Journal of Mathematical Sciences, Vol. 8, No.1, (2008), 61-66.
  • Generalized Lucas Sequence and Some Identities, Vikram Mathematical Journal, Vol. 28, (2008), 129-137.
  • Solution of “Problem B-1031”, The Fibonacci quarterly, Vol. 45, No. 2, (2007), 181: Published in The Fibonacci quarterly,  U. S. A., Vol. 45, No. 4, (2007), 371-372 and correction in Vol. 46/47, No. 1, (2008 /2009), 90.
  • Solution of “Problem B-1044”, The Fibonacci quarterly, Vol. 46/47, No. 1, (2008/2009), 85: Published in The Fibonacci quarterly, U. S. A., Vol. 46/47, No. 3, (2008/2009), 280-281.
  • Generalized Determinantal Identities Involving Lucas Polynomials”, Applied Mathematical Sciences, Bulgaria, Vol. 3, No. 8, (2009), 377-388.
  • Multiplicative Coupled Fibonacci Sequences and Some Fundamental Properties, International Journal of Contemporary Mathematical Sciences, Bulgaria, Vol. 5, No. 5, (2010), 223-230.
  • Fibonacci-Like Sequences and its Properties, International Journal of Contemporary Mathematical Sciences, Bulgaria, Vol. 5, No. 18, (2010), 859-868.
  • Coupled Fibonacci Sequences of Fifth order and Some Properties, International Journal of Mathematical Analysis, Bulgaria, Vol. 4, No. 25, (2010), 1247-1254.
  • Common Fixed Point Theorem for Expensive Maps in Menger Spaces through Compatibility, International Mathematical Forum, Bulgaria, Vol. 5, No. 63, (2010), 3147-3158.
  • Fibonacci-Triple Sequences and Some Fundamental Properties”, Tamkang Journal of Mathematics, Taiwan, Republic of China, Vol. 41, No. 4 (2010), 325-333.
  • Solution of “Problem B-1058”, The Fibonacci quarterly, Vol. 46/47, No. 4, (2008/09) Published in The Fibonacci quarterly, U. S. A., Vol. 48, No. 4, (2010), 369.
  • Some Trigonometric Identities of Fibonacci and Lucas Polynomials, Proceedings of National Seminar on “History of Mathematical Sciences” organized by Swami Vivekanand Govt P. G. College, Nimach, 2010.
  • Generalized Identities Involving Common Factors of Fibonacci and Lucas Numbers, International Journal of Algebra, Bulgaria, Vol.5, No. 13, (2011), 637-645.
  • Solution of “Problem B-1077”, The Fibonacci quarterly, Vol. 49, No. 4, (2010)  Published in The Fibonacci quarterly, U. S. A., Vol. 49, No. 4, (2011), 370-371.
  • Solution of “Problem B-1080”, The Fibonacci quarterly, Vol. 49, No. 4, (2010)  Published in The Fibonacci quarterly, U. S. A., Vol. 49, No. 4, (2011), 372-373.
  • Multiplicative Triple Fibonacci Sequences, Applied Mathematical Sciences, Bulgaria, Vol. 6, No. 52, (2012), 2567-2572.
  • Generalized Fibonacci-Like Polynomial and its Determinantal Identitites, International Journal of Contemporary Mathematical Sciences, Bulgaria, Vol. 7, No. 29, (2012), 1415-1420.
  • Multiplicative Coupled Fibonacci Sequences of Third order, International Journal of Contemporary Mathematical Sciences, Bulgaria, Vol. 7, No. 31, (2012), 1535-1540.
  • Generalized Fibonacci sequences, Theoretical Mathematics & Applications, Greece, Vol.2, No.2, (2012), 115-124
    Generalized Coupled Fibonacci Sequences, International Journal of Computer Applications (0975 – 8887), Volume 59– No.8, December 2012.
  • Generalized Fibonacci-Like Polynomials and its Determinantal Identities “International Journal of Contemporary Mathematical Sciences, Bulgaria, Vol. 7, (2012), No. 29, 1415-1420”, Bulgaria.
  • Generalized Fibonacci Sequences “Theoretical Mathematics & Applications, vol.2, no.2, 2012, 115-124”, United Kingdom.
    Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers “International Journal of Applied Mathematical Research, vol.1, no.4, 2012, 377-382”, Germany.
  • Identities of Fibonacci-Like Sequence “Journal of Mathematical and Computational Science, vol. 2, no. 6, 2012, 1801-1807” United Kingdom.
  • Some Identities of Generalized Fibonacci Sequences, “South pacific journal of Pure and Applied Mathematics, vol. 1, no. 1, 2012, 80-86” PNG.
  • Some Identities of Multiplicative Coupled Fibonacci Sequences, International Journal of Computer Applications (0975 – 8887), Volume 63– No.12, February 2013.
  • Fibonacci-Like Sequence, International Journal of Advanced Mathematical Sciences, Science Publishing Corporation, Germany, 1 (3), (2013), 145-151.
  • Fibonacci-Like Polynomials and Some Identities, International Journal of Advanced Mathematical Sciences, Science Publishing Corporation, Germany, 1 (3), (2013), 152-157.
  • Variations on domination in Graphs Containing Edge-Disjoint Cycles, Journal of Mathematical and computational Science, Science and Knowledge Publishing Corporation Limited, 3 (4), (2013), 1004-1014.
  • Generalized Identities of Companion Fibonacci-Like Sequences, Global journal of Mathematical Analysis, Science Publishing Corporation, 1(3), (2013), 104-109.
  • Generalized Fibonacci Sequence and its Properties, Open journal of Mathematical Modeling, Sciknow Publication Ltd., 1 (6), (2013), 194-202.
  • On Combinations of Higher Powers of Fibonacci-Like Sequence, “Open Journal of Mathematical Modeling, vol. 1, no. 2, 2013, 63-66” USA.
  • Generalized Identities Involving Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, “International journal of Analysis and Application, vol. 3, no. 1, 2013, 53-59”, CANADA.
  • Determinantal Identities for Generalized Fibonacci-Type Polynomials, “Open Journal of Mathematical Modeling, vol. 1, no. 5, 2013, 159-172” USA.
  • Generalized Fibonacci Polynomials, “Turkish Journal of Analysis and Number Theory, vol. 1, no. 1, 2013, 43-47” USA.
  • Identities of Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas Numbers, “Applied Mathematics and Physics, vol. 1, no. 4, 2013, 126-128” USA.
  • (1, 2) – Domination and Split Domination in Graphs, International Journal of Latest trends in Engineering and Technology (IJLTET), special issue – IEEDS 2013, 239-244.
  • Compatibility of type (P) and fixed point theorem in Fuzzy metric spaces, J. Math. Comput. Sci. Vol. 3, No. 3, 881-890, April 2013.
  • Generalized Fibonacci-Lucas Polynomials, International Journal of Advanced Mathematical Sciences, 2 (1) (2014) 81-87.
  • Sum Properties for the K-Lucas Numbers with Arithmetic Indexes, J. Math. Comput. Sci. 4 (2014), No. 1, 105-117
  • A Formula for Tetranacci-Like Sequence, Gen. Math., Notes, Vol. 20, No. 2, February 2014, 136-1414.
  • Generalized Fibonacci-Lucas Sequence and Its Properties, Global Journal of Mathematical, Analysis, 2 (3) (2014), 160-168.
  • Generalized Fibonacci-Like Polynomials and Some Identities, Global Journal of Mathematical, Analysis, 2 (4) (2014), 249-258.
  • Identities of Generalized Fibonacci-Like Sequence, Turkish Journal of Analysis and Number Theory, 2 (5) (2014), 170-175.
  • Fibonacci Polynomials and Determinant Identities, Turkish Journal of Analysis and Number Theory, 2 (5) (2014), 189-192.
  • Generalized Fibonacci-Lucas Sequence, Turkish Journal of Analysis and Number Theory, 2   (6) (2014), 193-197.
  • Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences, Turkish Journal of Analysis and Number Theory, 2 (6) (2014), 233-238.
  • k – Generalized Fibonacci Numbers, “ Applied Mathematics and Physics, vol. 2, no.1, 2014, 10-12” USA.
  • Generalized Fibonacci Sequences and Its Properties, “Palestine Journal of Mathematics, vol. 3, no. 1, 2014, 141-147”, PALESTINE.
  • Generalized bivariate Fibonacci-Like polynomials, “International Journal of Pure Mathematics, vol. 1, 2014, 08-13” USA.
  • Certain Properties of Generalized Fibonacci Sequence, “Turkish Journal of Analysis and Number Theory, vol. 2, no. 1, 2014, 6-8” USA.
  • On the k-Fibonacci-Like Numbers, “Turkish Journal of Analysis and Number Theory, vol. 2, no. 1, 2014, 9-12” USA.
  • On sums of odd and even terms of the K-Fibonacci numbers, “Global Journal of Mathematical Analysis, vol. 2, no. 3, 2014, 114-119” United Kingdom.
  • Fixed point theorem in intuitionistic Fuzzy metric spaces, International Journal of Advanced Technology in Engineering and Science Vol. 2, No. 7, 44-50, August 2014.
  • Common Factors of k-Fibonacci-Like, k-Fibonacci and k-Lucas numbers, “Journal of Research in Engineering & Technology, vol. 1, no. 2, 2015, 1-8” India.
  • Occasionally Weakly Compatible Mappings, Turkish Journal of Analysis and Number Theory,Vol. 3, No. 3, 78-82, July 2015.
  • On sums of odd and even terms of the Fibonacci Sequence, “Journal of Analysis and Number Theory, vol. 4, no. 1, 2016, 81-84” USA.

Paper Presentation in Conferences/Seminars:

  • Paper presented in the 72nd Annual conference of the Indian Mathematical Society held in Department of Mathematics & Computer Science, R. D. University, Jabalpur, during December 27 – 30, 2006.
    The title of paper: “Standard Proof Techniques for generalized Fibonacci sequence”
  • Paper presented in National Seminar on “Application of Mathematics Engineering & Technology” organized by Department of Applied Science, Madhav Institute of Technology & Science, Gwalior, India during February 2-3, 2008.
    The title of paper: “Some Determinantal Identities Involving Fibonacci Polynomials”
  • Paper presented in conference on “Recent Trends in the Advancement of Astronomy and Applied Mathematics” organized by S. G. R. R. (P.G.) College, Dehradun, Uttaranchal India during November 14-15, 2009.
    The title of paper: “Variations on Domination in Graphs Contain Edge-Disjoin Cycles”
  • Paper presented in conference on “Recent Developments in Applicable Mathematics & Information Technology” organized by Jaypee Institute of Engineering & Technology, Raghogarh, Distt. Guna (M. P.) during December 4-6, 2009.
    The title of paper: “Fibonacci Numbers and Domination Numbers of Graphs Contain Disjoin Cycles”.
  • Paper presented in 21st National Conference of Rajasthan Ganit Parishad on “Recent Trends in Mathematics and Actuarial Sciences” organized by Central University of Rajasthan and MNIT Jaipur at MNIT, Jaipur during February 20-21, 2010.
    The title of paper: “Some Properties of Generalized Fibonacci Polynomials”
  • Paper presented in National Seminar on “History of Mathematical Sciences” organized by Swami Vivekanand Govt P. G. College, Nimach at Nimach during February 26-27, 2010.
    The title of paper: “Generalization of Fibonacci Polynomials and Some Basic Properties”
  • Paper presented in National Conference organized by MPCST, Bhopal during 22-23 Feb., 2010.
    The title of paper: “Combinatorial Formulas Involving Fibonacci and Lucas Polynomials”.
  • Paper presented in National Seminar on “History of Mathematical Sciences” organized by Swami Vivekanand Govt P. G. College, Nimach at Nimach during February 26-27, 2010.
    The title of paper: “Some Trigonometric Identities of Fibonacci and Lucas Polynomials”.
  • Paper presented in National Conference on “Mathematical Modeling and Computer Simulation” organized by department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi during March 25-27, 2011.
    The title of paper: “Coupled Fibonacci Sequences of Third Order”
  • Paper presented in 14th International Conference (CONIAPS-XIV) on “Physical Sciences Interface with Humanity” organized by international Academy of Physical Sciences, National Institute of Technology, Surat during December 22-24, 2011.
    The title of paper: “Bivariate Fibonacci Polynomials”
  • Paper presented in National Conference organized by MPCST, Bhopal at JNKV, Jabalpur during Feb.28- March 1, 2011.
    The title of paper: “On Sums of Odd and Even Term of the Fibonacci sequence and Some Properties of the Fibonacci-Like Sequence”.
  • Paper presented in National Workshop-Cum-Conference on Recent Trends in Mathematics & Computing 2011, organized by The Technological Institute of Textile &
    Sciences, Bhiwani, Haryana May 21, 2011.
    The title of paper: “Combinatorial Formulas Involving Fibonacci Polynomials, Fibonacci-Like Polynomials and Fibonacci-Like Sequences”.
  • Paper presented in International Conference organized by CONIAPS, SURAT during 22-24, Dec., 2011.
    The title of paper: “Generalized Fibonacci Polynomial and Generalized Pell Polynomial”.
  • Paper presented in national Conference (AICTE Sponsored) on “Recent Advances in Mathematics with application in Engineering” organized by department of mathematics, government engineering college, Ajmer during March 12-13, 2012.
    The title of paper: “Generalized Bivariate Fibonacci Polynomials”.
  • Paper presented in National Conference organized by MPCST, Bhopal during 29Feb.- 1 March, 2012.
    The title of paper: “Generalized Fibonacci-Like Polynomials and its Determinantal Identities”.
  • Paper presented in National conference organized by Institute of Technology, Banaras Hindu University, Varanasi (U.P.) duration 23-25 March 2012.
    Title of paper: “Compatibility of Type (P) and Fixed Point Theorem in Fuzzy Metric Space”.
  • Paper presented in International Conference (AICTE Sponsored) on “Recent Advances in Mathematical Sciences and Application” (ICRAMSA-2013) organized by department of Applied Mathematics (University Institute of Technology), Rajiv Gandhi Proudyogiki Vishwavidyalaya (RGPV), Bhopal during December 24-26, 2013.
    The title of paper: “Generalized Fibonacci Polynomials ”.
  • Paper presented in National Conference organized by MPCST, Bhopal during 28Feb.- 1 March, 2013.
    The title of paper: “Generalized Fibonacci Sequences and Its Properties”.
  • Paper presented in International Conference organized by ICRAM, NAGPUR during 20-23, January, 2014.
    The title of paper: “On Sums of Odd and Even terms of the Fibonacci-Like Numbers”.
  • Paper presented in National Seminar organized by GMSPGC, Ujjain during 6- 7 March, 2014.
    The title of paper: “Some Properties of Generalized k-Fibonacci Numbers”
    (Awarded with best paper ).
  • Paper presented in International conference organized by RastrasantTukdojiMaharaj, Nagpur  University, Nagpur (Maharastra) duration 20 – 23 January, 2014.
    Title of paper: “Fixed Point Theorem in Fuzzy Metric Space through weak compatibility”.
  • Paper presented in National conference organized by M. science collage, Ujjain, (M.P)duration 6 – 7 March, 2014.
    Title of paper: “Fixed Point Theorem in Fuzzy Metric Space through semi compatibility”.
  • Paper presented in National Conference on Computational Mathematics in Engineering and 26th Annual Conference of Rajasthan Ganita Parishad (NCCME-RGP-2015) organized by department of Mathematics, Rajasthan Technical University (RTU), Kota during 23-02-2015 to 24-02-2015.
    The title of paper: “Domination Numbers of Graphs Containing Vertex-Disjoint Cycles”.
  • Paper presented in National Conference organized by MPCST, Bhopal during 28Feb.- 1 March, 2015.
    The title of paper: “Generalized k-Fibonacci Numbers and its Properties”.
    (Awarded fellowship for training of Young Scientist of M.P. Council of Science & Technology).
  •  Paper presented in International conference organized by MANIT Bhopal duration (M.P) 11-14 December, 2015.
    Title of paper: “Compatibility and (OWC) Mappings”.
  • Paper presented in National conference organized by RMS Bareilly (U.P) duration 22-24 January, 2016.
    Title of paper: “Semi Compatibility Mapping of Fuzzy Metric Space”.

Book publication:
Title: GENERALIZATION OF FIBONACCI SEQUENCE – An intriguing Sequence
Publisher: LAP LAMBERT Academic Publishing GmbH & Co. KG, Germany
Author: Dr. OMPRAKASH SIKHWAL
Year: 2012.

Title: GENERALIZED FIBONACCI SEQUENCE
Publisher: LAP LAMBERT Academic Publishing GmbH & Co. KG, Germany
Author: Dr. YASHWANT K. PANWAR
Year: 2012.

Title: A FIBONACCI-LIKE SEQUENCE (An Elegant Sequence)
Publisher: LAP LAMBERT Academic Publishing GmbH & Co. KG, Germany
Author: Dr. YASHWANT K. PANWAR
Year: 2013.

Title: GENERALIZATION OF FIBONACCI POLYNOMIALS
Publisher: Kartindo Academia, India (International Publisher and distributor)
Author: Dr. OMPRAKASH SIKHWAL
Year: 2014.