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Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

100%

Yamaod O., Sintunavarat W., Je Cho Y.

Open Mathematics

2016

tom 14

nr 1

128-145

In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫ a b K 1 (t,r,x(r)) dr, x (t) = ∫ a b K 2 (t,r,x(r)) dr, $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$ where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.

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Fixed point theorem in 2 non-archimedean Menger PM-Space using weakly L-compatible and weakly M-compatible mappings

100%

Gupta V. K., Jain A., Kushwah J.

Commentationes Mathematicae

2011

tom 51

nr 2

In the present paper, we extend and generalize the result of Cho et. al. [1] by introducing the notion of weakly L-compatible and weakly M-compatible maps in a 2 non-Archimedean Menger PM-space.

Semi-compatibility in non-archimedean Menger PM-space

100%

Singh B., Jain A., Agarwal P.

Commentationes Mathematicae

2009

tom 49

nr 1

The object of this paper is to establish fixed point theorem for six self maps and an example using the concept of semi-compatible self maps in a non-Archimedean Menger PM-space. Our result generalizes the result of Cho et. al. [2].

Ograniczanie wyników

2 Commentationes Mathematicae

1 Open Mathematics

2 Jain A.

1 Agarwal P.

1 Gupta V. K.

1 Je Cho Y.

1 Kushwah J.

1 Singh B.

1 Sintunavarat W.

1 Yamaod O.

1 2016

1 2011

1 2009

Wyniki wyszukiwania

Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

Fixed point theorem in 2 non-archimedean Menger PM-Space using weakly L-compatible and weakly M-compatible mappings

Semi-compatibility in non-archimedean Menger PM-space