• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.13-33
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• 2021

The aim of this paper is to establish common fixed point theorems under generalized (ψ - ϕ)-weak contractions in the setting of complete S-metric spaces and we support our result by some examples. Also an application of our results, we obtain some fixed point theorems of integral type. Our results extend Theorem 2.1 and 2.2 of Doric [5], Theorem 2.1 of Dutta and Choudhury [6], and many other several results from the existing literature.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.517-526
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• 2024

In this paper, some iterative methods are used to discuss the behavior of general mixed-harmonic variational inequalities. We employ the auxiliary principle technique and g-strongly harmonic monotonicity of the operator to obtain results on the existence of solutions to a generalized class of mixed harmonic variational inequality.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.175-203
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• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.289-308
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• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.137-155
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• 2021

In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Finally, we give some applications of our results in discrete and functional fractional economic systems.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.957-988
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• 2023

We define new classes of expansive-type mappings in the setting of modular 𝜔^G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔^G-complete modular 𝜔^G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.663-673
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• 2007

This paper presents a new moving obstacle detection method using an optical flow in mobile robot with an omnidirectional camera. Because an omnidirectional camera consists of a nonlinear mirror and CCD camera, the optical flow pattern in omnidirectional image is different from the pattern in perspective camera. The geometry characteristic of an omnidirectional camera has influence on the optical flow in omnidirectional image. When a mobile robot with an omnidirectional camera moves, the optical flow is not only theoretically calculated in omnidirectional image, but also investigated in omnidirectional and panoramic images. In this paper, the panoramic image is generalized from an omnidirectional image using the geometry of an omnidirectional camera. In particular, Focus of expansion (FOE) and focus of contraction (FOC) vectors are defined from the estimated optical flow in omnidirectional and panoramic images. FOE and FOC vectors are used as reference vectors for the relative evaluation of optical flow. The moving obstacle is turned out through the relative evaluation of optical flows. The proposed algorithm is tested in four motions of a mobile robot including straight forward, left turn, right turn and rotation. The effectiveness of the proposed method is shown by the experimental results.