Some theorems for a new type of multivalued contractivemaps on metric space

Abstract

In this paper, taking into account the function θ , we introduce a new type of contraction for multivalued maps on metric space. This new concept includes many known contractions in the literature. We then present some fixed point results for closed and bounded set valued maps on complete metric space. Finally, we provide an example to show the significance of the investigation of this paper.

Fixed Points for Multivalued Suzuki Type (θ,R)-Contraction Mapping with Applications

“…Durmaz [7] introduced a new type of generalized multivalued -contraction and proved some interesting fixed point results (see also [8]). Kikkawa and Suzuki [9] refined Nadler' result by proving the following theorem.…”

Fixed Point Theorems for Set-ValuedL-Contractions in Branciari Distance Spaces

“…Remark 14. Corollary 13 is a generalization of Theorem 2 of [44] to Branciari distance spaces with conditions:…”

Common Fixed Points of(α,η)−(θ,ϝ)Rational Contractions with Applications

“…For further results in this direction, we refer to [7][8][9][10]. Another variation of contraction mapping that can be found in literature is -contraction mapping.…”