Make unification on α -admissible mappings and related fixed point theorems

Abstract

In this paper, we introduced the concepts pair (F , h) a upclass of type II and α β -contractive mappings and show that theorems in [4]reduce to corollaries in this paper. that is, all them can obtain of one theorem. in end we state example for support main result.

Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions

“…Definition 2.10 ( [4,6]). We say that h : R + × R + → R is a function of subclass of type I if it satisfies…”

“…Definition 2.12 ( [4,6]). Let h, F : R + × R + → R. We say pair (F, h) is a upper class of type I if F is a function, h is a subclass of type I and…”

Pair (F,h) upper class and (\alpha ,\mu)-generalized multivalued rational type contractions

“…Very recently, Karapinar et al [11] gave a new type of rational contraction condition for multivalued mappings. In this paper, we combine the ideas of Karapinar et al [11] and Ansari [6], to introduce contraction conditions which are even more general than the condition given by the Karapinar et al [11]. Then by using our new contraction conditions we prove fixed point theorems which give us many other new results in different dimensions.…”

“…The notion of the pair (F, h) is an upper class which was introduced by Ansari et al [6,7]. He involved this pair in a contraction condition and proved a fixed point theorem which generalized many existing results.…”

Upper class of type I on coupled coincidence point results for some contractions in partially ordered JS-metric spaces

“…In 2017, Phudolsitthiphat and Wiriyapongsanon [6] extended the result in [4] to find a coupled coincidence point of α-Geraghty contractions under JS-metric spaces. Next, Ansari and Shukla [1,2] gave the idea of a relation between F and h, precisely, the pair (F , h) to be an upper class.…”