Common fixed point results of generalized almost rational contraction mappings with an application

Abstract

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common fixed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the presented results.

Fixed point theorems for quadruple self-mappings satisfying integral type inequalities

“…Inspired from the work of the scientists [20][21][22][23][24][25][26][27][28][29][30][31], in this paper, we further extend the notion of generalized almost (S, F )-rational contraction pair (h, ) to the generalized almost (S, F , Γ)-rational contraction pair (h, ) of integral type and prove some new fixed point theorems. Our results generalize the work in [24] and many others in the literature. Definition 1.2.…”

“…Definition 1.3. [24] Generalized altering distance function is a mapping τ : R + → R + , satisfying that: (i) τ is non-decreasing;…”

“…Recently, Hussein et al [24] introduced the notion of cyclic (α, λ)-admissible pair of maps (h, ) on a metric space (X, d) and defined generalized almost (S, F )-rational contraction pair (h, ), as below: Definition 1.4. [24] Let h, , S and F be quadruple self-mappings of a nonempty set X and α, λ :…”

“…Definition 1.5. [24] Let h, , S, F be self maps of a metric space (X, d), and (h, ) be a cyclic (α, λ) (S,F ) -admissible pair. We say that (h, ) is a generalized almost (S, F )-rational contraction pair if…”

“…Theorem 1.6. [24] Let h, , S, F be self mappings of a complete metric space (X, d) with h(X) ⊂ F (X), (X) ⊂ S(X) and (h, ) be a generalized almost (S, F )-rational contraction pair. Suppose that: (a) there exist µ * 0 ∈ X such that α(Sµ * 0 ) ≥ 1 and λ(F…”