• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.817-825
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability of the following cubic funtional equation f(2x + y) + f(2x - y) = 2f(x + 2y) - 4f(x + y) + 18f(x) - 12f(y) by the direct method in 2-normed spaces.

• 대한수학회논문집
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• 제28권2호
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• East Asian mathematical journal
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• 제24권1호
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• pp.57-65
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• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.93-104
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• 2021

In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadžić type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.663-677
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• 2022

This present paper extends some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Kannan type mappings. Non-trivial examples are further provided to support the hypotheses of our results.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.295-309
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• 2023

In this paper, we introduce the notion of α-Geraghty contractive type covariant and contravariant mappings in the bipolar metric spaces. In addition, we prove some fixed point theorems, which give existence and uniqueness of fixed point, for α-Geraghty contractive type covariant and contravariant mappings in complete bipolar metric spaces. Finally, we show some examples to support our main results.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.311-335
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• 2023

Fixed point theory is the center of focus for many mathematicians from last few decades. A lot of generalizations of the Banach contraction principle have been established. In this paper, we introduce the concepts of 𝜃-contraction and 𝜃-𝜑-contraction in quasi-metric spaces to study the existence of the fixed point for them.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.233-247
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• 2022

In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, d_b). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1097-1113
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• 2023

In this paper, we extend some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Hardy-Roger type mappings. Our result generalizes many known results in fixed point theory. Finally, we offer a example to illustrate our result.