A novel kind of Hermite based Frobenius type Eulerian polynomials
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An open problem and an example is given to justify the im- portance of our main result.
Abstract
After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An open problem and an example is given to justify the im- portance of our main result.
참고문헌 (19)
- Bell, E. T, "Exponential polynomials", Ann. of Math, 35, pp.258~277 (1934)
- Carlitz, L, "Eulerian numbers and polynomials", Math. Mag, 32, pp.247~260 (1959)
- Carlitz, L, "Eulerian numbers and polynomials of higher order", Duke Math. J, 27, pp.401~423 (1960)
- Choi, J, "A note on some identities of Frobenius-Euler numbers and polynomials", Inter. J. Math. Math. Sci., 2012, pp.1~9 (2012)
- Dattoli, G, "Finite sums and generalized forms of Bernoulli polyno-mials", Rendiconti di Mathematica, 19, pp.385~391 (1999)
- Waseem Ahmad Khan, "Some Properties of the Generalized Apostol Type Hermite- Based Polynomials", Kyungpook Mathematical Journal, 55(3), pp.597~614 (2015), 경북대학교 자연과학대학 수학과
- 김대산, "A note on Eulerian polynomials associated with Bernoulli and Euler numbers and polynomials", Advanced Studies in Contemporary Mathematics, 22(3), pp.379~389 (2012), 장전수학회[DOI]
- Kim, D. S, "A note on Eulerian polynomials", Abtr. Appl. Anal, pp.10~ (2012)
- Kim, D. S, "Some new identities of Frobenius-Euler numbers and polynomials", J. Ineq. Appl., 2012, pp.1~10 (2012)
- Kurt, B, "On the generalized Apostol type Frobenius Euler polynomials", Advances in Differences equations, pp.1~9 (2013)
- Kurt, B, "Frobenius Euler type polynomials related to Hermite-Bernoulli polynomi-als", Proceedings of the International Conferences on Numerical Analysis and Applied Mathematics, Amer, Inst. Phys. Conf. Proc., 1389, pp.385~388 (2011)
- Pathan, M. A, "Some implicit summation formulas and symmetric identities for the generalized Hermite-based polynomials", Acta Universitatis Apulensis, 39, pp.113~136 (2014)
- Pathan, M. A, "Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials", Mediterr. J. Math, 12, pp.679~695 (2015)
- Pathan, M. A, "A new class of generalized polynomials associated with Hermite and Euler polynomials", Mediterr. J. Math, 13, pp.913~928 (2016)
- Pathan, M.A, "Some implicit summation formulas and symmetric identities for the generalized Hermite-Euler polynomials", East-West J. Maths, 16(1), pp.92~109 (2014)
- Srivastava, H. M, "Eulerian and other integral representations for some families of hypergeometric polynomials", Inter. J. Appl. Math. Stat., 11, pp.149~171 (2007)
- Srivastava, H. M, "A treatise on generating functions" (1984), Ellis Horwood Limited
- Srivastva, H. M, "A class of Frobenius-type Eulerian polynomials", Rocky Mountain J. Math., 48, pp.1003~1013 (2018)
- Simsek, Y, "Generating functions for generalized Stirlings type numbers array type polynomials, Eulerian type polynomials and their application", Fixed Point Theory and Appl. (2013)[DOI]