Bangmod International Journal of Mathematical and Computational Science

SOLUTION OF INTEGRAL EQUATION INVOLVING INTERPOLATIVE ENRICHED CYCLIC KANNAN CONTRACTION MAPPINGS

Mujahid Abbas — 2023-12-31

The purpose of this paper is to introduce the class of interpolative enriched cyclic Kannan contraction mappings deﬁned on an Banach space and to prove the existence and uniqueness of ﬁxed point of the such mappings. An example is presented to support the concept introduced herein. Moreover, an application of the main result to solve nonlinear integral equations is also given. Our result extend and generalize various results in the existing literature.

ON L-FUZZY FIXED POINT RESULTS IN G-METRIC SPACE

Hafiz Muhammad Zeeshan — 2023-12-31

Among numerous efforts in progressing fuzzy mathematics, a lot of attention has been paid to studying new L-fuzzy analogues of the conventional fixed point results and their various applications. In this note, novel concepts of L-fuzzy contractions in G-metric space is examined, and sufficient conditions for the existence of L-fuzzy fixed points for such mappings are investigated. Nontrivial examples are provided to support the assumptions of our obtained theorems. It is highlighted that the main ideas studied herein refine and include some known results in the corresponding literature. Some of these special cases of our results are pointed out and analyzed.

A HYBRID CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION WITH APPLICATION

Nasiru Salihu — 2023-12-31

This article considers a hybrid minimization algorithm from optimal choice of the modulating
non-negative parameter of Dai-Liao conjugacy condition. The new hybrid parameter is selected in such
away that a convex combination of Hestenes-Stiefel and Dai-Yuan Conjugate Gradient (CG) algorithms
is fulfilled. The numerical implementation adopts inexact line search which reveals that the scheme is
robust when compared with some known efficient algorithms in literature. Furthermore, the theoretical
analysis shows that the proposed hybrid method converges globally. The method is also applicable to
solve three degree of freedom motion control robotic model.

APPROXIMATION METHOD FOR COMMON FIXED POINT OF A COUNTABLE FAMILY OF MULTI-VALUED QUASI-ϕ-NONEXPANSIVE MAPPINGS IN BANACH SPACES

Adamu Inuwa — 2023-12-31

In this paper, we study a new iterative algorithm to approximate a common fixed point of a
countable family of multi-valued quasi-φ nonexpansive mappings in a uniformly smooth and uniformly
convex real Banach space. We prove strong convergence theorem which improve and generalize recently
announced results in the literature. We also give some example to illustrate our theorem and we also
give application to zero point problem of maximal monotone mappings

GUARANTEED PURSUIT TIME OF A LINEAR DIFFERENTIAL GAME WITH GENERALIZED GEOMETRIC CONSTRAINTS ON PLAYERS CONTROL FUNCTIONS

Ahmad Yahaya Haruna — 2023-12-31

In this study, simple motion differential game of one pursuer and one
evader is considered in Rn. Control functions of the players are subject to
more generalized geometric constraints. Pursuit is said to be completed
at a finite time Γ whenever the distance between both players at time Γ
is zero.We obtain an estimate for the guaranteed pursuit time Γ and construct
pursuer’s strategy that ensure completion of pursuit at the time Γ.

DESCENT MODIFIED CONJUGATE GRADIENT METHODS FOR VECTOR OPTIMIZATION PROBLEMS

Jamilu Yahaya — 2023-12-31

Scalarization approaches transform vector optimization problems (VOPs) into single-objective optimization. These approaches are quite elegant; however, they suffer from the drawback of necessitating the assignment of weights to prioritize specific objective functions. In contrast, the conjugate gradient (CG) algorithm provides an attractive alternative that does not require the conversion of any objective function or assignment of weights. Nevertheless, the set of Pareto-optimal solutions is obtainable. We introduce three CG techniques for solving VOPs by modifying their search directions. We consider modifying the search directions of the Fletcher-Reeves (FR), conjugate descent (CD), and Dai-Yuan (DY) CG techniques to obtain their descent property without the use of any line search, as well as to achieve good convergence properties. Numerical experiments are conducted to demonstrate the implementation and efficiency of the proposed techniques.

AN ALGORITHM FOR APPROXIMATING SOLUTIONS OF SPLIT HAMMERSTEIN INTEGRAL EQUATIONS

Abdulmalik Usman Bello — 2023-12-31

In this paper, we introduce split Hammerstein integral equations of the form: u ∈ H_1 such

that u + K_1F_1u = 0 and A(u) + K_2F_2(Au) = 0, where K_1, F_1 are maximal monotone maps defined on

a real Hilbert space H_1, with D(K_1) = D(F_1) = H_1; K_2, F_2 are maximal monotone maps defined on a

real Hilbert space H_2, with D(K_2) = D(F_2) = H_2 and A, a bounded linear map from H_1 to H_2. The sequence of the algorithm is proved to converge strongly to a solution of the split Hammerstein integral equation. As far as we know, this is the first algorithm whose sequence approximates a solution of a split Hammerstein integral equation in this direction. Finally, the theorem proved, improves and complements some important related recent results in the literature.