Browsing by Author "Wahab, O. T."

Now showing 1 - 11 of 11
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    Common Coupled Fixed Point Theorems without Compatibility in Partially Ordered Metric Spaces
    (International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2022-06-30) Tijani, K. R.; Wahab, O. T.; Usamot, I. F.; Alata, S. M.
    A perfect blend of requirements for the proof of common coupled fixed point theorems in partially ordered metric space without the assumptions of (weak) compatibility is accomplished. Previous attempts in this direction involving these assumptions mostly ensure existence of coupled coincidence points. In many existing works in this area, attempt have been made to prove the existence of common coupled fixed points. However, only identity mappings can satisfy the conditions of the theorems. The method of proof presented in this present work is powerful in view of the fact that it guarantees the existence of common coupled fixed points without the imposition of (weak) compatibility conditions and identity mappings. To illustrate the results, an example is provided.
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    Continuous Dependence for Two Implicit Kirk-Type Algorithms in General Hyperbolic Spaces
    (Hindawi Publishing Corporation, 2017-06-21) Rauf, K.; Wahab, O. T.; Alata, S. M.
    This paper aims to study extensively some results concerning continuous dependence for implicit Kirk-Mann and implicit Kirk- Ishikawa iterations. In order to equipoise the formation of these algorithms, we introduce a general hyperbolic space which is no doubt a free associate of some known hyperbolic spaces. The present results are extension of other results and they can be used in many applications.
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    Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces
    (Hindawi Publishing Corporation, 2016-09-09) Wahab, O. T.; Olawuyi, R. O.; RAUF, K.; Usamot, I. F.
    This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature.
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    Finite Element Methods on Derivative Least–Square and Semi-Standard Galerkin for Solving Boundary Value Problems
    (The Pacific Journal of Science and Technology, Akamai University, 2015-11-15) Rauf, K.; Omolehin J. O.; Aniki, S. A.; Wahab, O. T.
    In this paper, we derived a Derivative Least–Square Method (DLSM) and Semi-Standard Galerkin Method (SSGM) which are both Finite Element Methods (FEM) for Solving Boundary Value Problems. In the DLSM, the residue was differentiated into a new derivative of the residue R while in the SSGM, we took I, for which D is its basis function. The proposed methods were applied on several boundary value problems and the numerical results obtained are reliable and in good agreement with the exact solutions.
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    NEW IMPLICIT KIRK-TYPE SCHEMES FOR GENERAL CLASS OF QUASI-CONTRACTIVE OPERATORS IN GENERALIZED CONVEX METRIC SPACES
    (Austral Internet Publishing, 2017-04-11) Rauf, K.; Wahab, O. T.; Ali, A.
    In this paper, we introduce some new implicit Kirk-type iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasi-contractive type operators. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.
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    On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators
    (Hindawi Publishing Corporation, 2016-07-26) Wahab, O. T.; Rauf, K.
    The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybridKirk-Multistep iterative schemes in the literature.
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    ON GENERAL CLASS OF NONLINEAR CONTRACTIVE MAPS AND THEIR PERFORMANCE ESTIMATES
    (Austral Internet Publishing, 2021-12-06) Wahab, O. T.; Musa, S. A.
    This paper considers two independent general class of nonlinear contractive maps to study the existence properties of nonlinear operators with prior degenerate. The existence properties are proved in the framework of approximate fixed points with the imposition of the general class of contractive conditions in metrical convex spaces without emphasis on completeness or compactness. For computational purposes, the performance estimates and the sensitivity dependence of these conditions are obtained for the Picard operator. Practical examples are also considered to justify the validity of the conditions. The results ensure no term is lost in the operators with prior degenerate and the conditions are strictly larger class when compare with others in the literature.
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    On Nonexpansive and Expansive Semigroup of Order-Preserving Total Mappings in Waist Metric Spaces
    (Nigerian Society of Physical Sciences, 2022-12-22) Usamot, I. F.; Wahab, O. T.; Alata, S. M.; Tijani, K. R.
    In this paper, we introduce nonexpansive and expansive semigroup of order-preserving total mappings (ONTn) and (OETn), respectively, to prove some fixed point theorems in waist metric spaces. We examine the existence of mappings that satisfy the conditions ONTn and OETn. We also prove that every semigroup of order-preserving total mappings OTn has fixed point properties and that the set of fixed points is closed and convex. The present study generalised many previous results on semigroup of order-preserving total mappings OTn. E cacy of the results was justified with some practical examples.
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    On v-quasi-Geraghty Contractive Mappings and Application to Perturbed Volterra and Hypergeometric Operators
    (Kyungpook Mathematical Journal, 2023-03-31) Wahab, O. T.
    In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.
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    SOME RESULTS ON COMMON FIXED POINT FOR GENERALIZED f-CONTRACTION MAPPING
    (Global Journal of Mathematics, 2015-03-20) Alata, S. M.; Rauf, K.; Wahab, O. T.
    In this article, we prove some common fixed point theorems for the generalized f-contraction mapping in a complete cone metric space. Our results extend and generalized some recent results.
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    SOME RESULTS ON IMPLICIT MULTISTEP FIXED POINT ITERATIVE SCHEMES FOR CONTRACTIVE-LIKE OPERATORS IN CONVEX METRIC SPACES
    (Universiteti i Prishtin es, Prishtine, Kosove., 2018-08-14) Wahab, O. T.; Rauf, K.
    In this paper, we establish and prove strong convergence, T-stability, convergence rate and data dependence results for multistep xed point iterative schemes using a class of contractive-like operators in convex metric spaces. Our results show that the proposed implicit multistep schemes have better convergence rate than the well-known explicit multistep schemes and multistep SP-iterative schemes. This is shown by analytical processes and validated with numerical examples. Several known results in the literature are embedded in these present results.