Existence theorem for integral inclusions by a fixed point theorem for multivalued implicit-type contractive mappings

Abstract

In this article, we introduce fixed point theorems for multivalued mappings satisfying implicit-type contractive conditions based on a special form of simulation functions. We also provide an application of our result in integral inclusions. Our outcomes generalize/extend many existing fixed point results.

Fixed Point Results for Single and Multivalued Maps on Partial Extended b -Metric Spaces

“…Fixed point theorems are developed for single-valued or set-valued mappings of abstract metric spaces. One can see a lot of literature on metric fixed point theory [1][2][3][4][5][6][7][8][9]. Recently, Shukla and Panicker [10] investigated some fixed point results on generalized enriched nonexpansive mappings defined on Banach spaces.…”

“…Shukla [18] presented the notion of a partial b-metric space and proved some related fixed point results. A lot of research can be seen in literature on b-metric spaces (see [1,2,7,8,[19][20][21][22][23]), which is a stimulation towards the concept of extended b-metric spaces introduced by Kamran et al [6] who proved the Banach contraction theorem in the setting of extended b-metric spaces. Afterwards, many authors have focused on the subject and generalized different results of metric spaces in extended b-metric spaces (see [3,[24][25][26][27][28]).…”

On interpolative F-contractions with shrink map

“…Altun and Tasdemir [9] presented the study of best proximity points using interpolative proximal contraction inequalities. Along with the aforementioned studies, many other interesting studies on fixed point theory are available in [10][11][12][13][14][15][16][17][18][19][20][21][22][23]; they help readers to verify the existence of fixed points for self-mappings and best proximity points for nonself mappings. Jleli et al [23] introduced the concept of E-fixed point (also called φ-fixed point), which states that, for maps V : K → K and E : K → [0, ∞), a point k ∈ K is called E-fixed point of V : K → K if V (k) = k and E(k) = 0, and proved the existence of such points by using a single inequality involving both maps V and E. It is important to note that Jleli et al [23] used the lower semicontinuity of E. This use of the lower semicontinuity of E by Jleli et al [23] arises the question whether the condition of lower semicontinuity of E can be left and some other technique be adopted.…”