Abstract
The aim of this paper is to present several fixed-point results for L-contractive multivalued mappings involving θ-functions in the class of metric spaces. We also give some examples in support of the related concepts and presented results. A homotopy result is also provided.
Highlights
1 Introduction Fifty years ago, Nadler [1] introduced the idea of multivalued contraction mappings and presented his famous result, which generalized the Banach contraction principle [2] for multivalued mappings
In [3], the authors studied a problem of a global optimization using a common best proximity point of a pair of multivalued mappings
Several research works in fixed point theory related to multivalued contractions in different areas have appeared
Summary
Nadler [1] introduced the idea of multivalued contraction mappings and presented his famous result, which generalized the Banach contraction principle [2] for multivalued mappings. Debnath and Srivastava [4] introduced a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. Let (X, d) be a metric space and denote by CB(X) the family of nonempty, bounded, and closed subsets of X. H( 1, 2) = max sup d(a, 2), sup d(b, 1) , a∈ 1 b∈ 2 where d(a, 2) = inf{d(a, ρ) : ρ ∈ 2}. Such a function H is called the Hausdorff–Pompieu metric induced by the metric d. Denote by CL(X) the family of nonempty and closed subsets of X and by K(X) the family of nonempty and compact subsets of X. A new type of a contraction mapping, known as an θ -contraction, was introduced by Jleli and Samet [24]
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