Fixed Point of Generalized Weak Contraction in -Metric SpacesRead the full article
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A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties
In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called degenerate poly-Genocchi polynomials and numbers, by using the degenerate polylogarithm function, and we derive several properties of these polynomials systematically. Then, we also consider the degenerate unipoly-Genocchi polynomials attached to an arithmetic function, by using the degenerate polylogarithm function, and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.
Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions
It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If denotes the class of functions analytic and univalent in the open unit disk , then the logarithmic coefficients of the function are defined by . In the current paper, the bounds for the logarithmic coefficients for some well-known classes like for and were estimated. Further, conjectures for the logarithmic coefficients for functions belonging to these classes are stated. For example, it is forecasted that if the function , then the logarithmic coefficients of satisfy the inequalities Equality is attained for the function , that is,
Periodic and Fixed Points for Caristi-Type -Contractions in Extended -Gauge Spaces
In this paper, we introduce extended -gauge spaces and the extended family of generalized extended pseudo--distances. Moreover, we define the sequential completeness and construct the Caristi-type -contractions in the framework of extended -gauge spaces. Furthermore, we develop periodic and fixed point results in this new setting endowed with a graph. The obtained results of this paper not only generalize but also unify and improve the existing results in the corresponding literature.
On Suzuki and Wardowski-Type Contraction Multivalued Mappings in Partial Symmetric Spaces
The purpose of this paper is to provide some fixed-point results for Suzuki and Wardowski-type contraction multivalued mappings in partial symmetric spaces. We give some examples to support and substantiate the developed notions and obtained results. Also, we use one of our main results to establish the existence and uniqueness of the solution for a system of integral inclusions.
Coincidence Point Results on Relation Theoretic -Contractions and Applications
Motivated by the ideas of -weak contractions and -contractions, the notion of -contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for -contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.