Existence theorems of a new set-valued MT-contraction in b-metric spaces endowed with graphs and applications

Abstract

A new concept of set-valued Mizoguchi-Takahashi G-contractions is introduced in this paper and some fixed point theorems for such mappings in b-metric spaces endowed with directed graphs are established under some sufficient conditions. Our results improve and extend those of [20] and [24]. We also give some examples supporting our main results. As an applications, we prove the existence of fixed points for multivalued mappings satisfying generalized MT-contractive condition in-chainable b-metric spaces and the existence of a solution for some integral equations.

TOPOLOGI DI RUANG METRIK PSEUDO-b_s

“…memperbaiki tulisannya dengan menambahkan satu teorema yang menunjukkan eksistensi titik tetap dengan syarat fungsi f k : X → R, dengan definisi f k (x) = d k (x, T (x)) untuk setiap x ∈ X dan T merupakan fungsi bernilai himpunan dari X ke keluarga semua himpunan bagian tertutup-F dari X yang tidak kosong, merupakan fungsi semikontinu bawah untuk setiap k ∈ N [3]. Selain itu, dalam tulisan-tulisan lainnya yang merujuk ke [2], yaitu [1,5,6,8,9,10], dibahas mengenai eksistensi titik tetap di ekstensi ruang metrik-b dengan metode yang berbeda-beda. Nosheen Zikria, dkk.…”

Some PPF Dependent Fixed Point Theorems for Generalized α-F-Contractions in Banach Spaces and Applications

“…A graph G is said to be connected if there is a path between any two vertices. The graph G is said to be weakly connected ifG is connected (for more details, see [5,9,11,27,28]). Definition 15 ([11]).…”

Several Fixed Point Theorems in Convex b-Metric Spaces and Applications

“…Subsequently, Boriceanu, Bota and Petrusel [19,20] obtained some concrete examples of b-metric spaces, and studied the fixed point properties of set-valued operators in b-metric spaces. The fixed point properties of b-metric spaces have received much attention; for example, see [21][22][23][24][25][26][27][28] and references therein.…”