Fixed point theorems for generalized (beta-phi)-contractive pair of mappings using simulation functions

Abstract

In this paper, our aim is to present a new class of generalized (beta-phi)-Z- contractive pair of mappings and we prove certain xed point theorems for a pair of mappings using this concept. Our results generalizes some xed point theorems in the literature. As an application some xed point theorems endowed with a partial order in metric spaces are also proved.

Common Fixed Point Theorems for Generalized Contractive Pair of Mappings in a Metric Space and Their Application to Fractional Calculus

“…In this paper, we have extended and generalized the results proved by Kumar and Sharma in [23] in 2021. Our current study provides a new approach for proving fixed point results in terms of binary relation by relaxing the condition of existing a subsequence for some convergent sequence and modifying the condition of β-admissibility.…”

“…Our results show some fixed point results for generalized β − ϕ − Zcontractive pair of mappings in a new manner using the conditions in terms of R-continuity and relation R in terms of closeness of functions. We also explore an example (Example 21) which shows that our results are better in comparison to the existing result [23]. In addition, we have attained the existence and the uniqueness of the solution of fractional differential equations in the context of our main result, and hence our study is also proved to be useful in finding the existence and the uniqueness 2…”

“…Definition 12 (see [23]). Consider a metric space ðS, σÞ and two self-mappings U, V : S ⟶ S. Then, the pair ðU, VÞ is said to be generalized β − ϕ − Z-contractive pair of mappings with respect to ξ if…”

“…Recently, Sarwar et al [22] have proposed some fixed point results in metric interval and normed interval spaces using the concept of simulation functions and α-admissibility in 2021. Also, in 2021, Kumar and Sharma [23] illustrated the idea of generalized α − ϕ − Z-contractive type mapping and proved some fixed point results in metric spaces. Here, the results are proved in terms of α-admissibility condition and a condition of exis-tence a subsequence for some convergent sequence and for the validity of their results; they have also demonstrated some fixed point results in metric spaces endowed with a partial order.…”