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Latest Published Articles

On a class of \(p\)-valent functions with negative coefficients defined by opoola differential operator

OMA-Vol. 6 (2022), Issue 2, pp. 35 – 50 Open Access Full-Text PDF
Bitrus Sambo and Timothy Oloyede Opoola

Abstract:Using opoola differential operator, we defined a subclass \(S^{n}_{p}(\lambda,\alpha,\gamma,\delta)\) of the class of multivalent or p-valent functions. Several properties of the class were studied, such as coefficient inequalities, hadamard product, radii of close-to-convex, star-likeness, convexity, extreme points, the integral mean inequalities for the fractional derivatives, and further growth and distortion theorem are given using fractional calculus techniques.

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Results of semigroup of linear operators generating a nonlinear Schrödinger equation

OMA-Vol. 6 (2022), Issue 2, pp. 29 – 34 Open Access Full-Text PDF
J. B. Omosowon, A. Y. Akinyele and F. Y. Aderibigbe

Abstract:In this paper, we present results of \(\omega\)-order preserving partial contraction mapping generating a nonlinear Schr\”odinger equation. We used the theory of semigroup to generate a nonlinear Schr\(\ddot{o}\)dinger equation by considering a simple application of Lipschitz perturbation of linear evolution equations. We considered the space \(L^2(\mathbb{R}^2)\) and of linear operator \(A_0$ by $D(A_0)=H^2(\mathbb{R}^2)\) and \(A_0u=-i\Delta u\) for \(u\in D(A_0)\) for the initial value problem, we hereby established that \(A_0\) is the infinitesimal generator of a \(C_0\)-semigroup of unitary operators \(T(t)\), \(-\infty

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On generalized Tetranacci numbers: Closed forms of the sum formulas \(\sum\limits_{k=0}^{n}kx^{k}W_{k}\) and \(\sum\limits_{k=1}^{n}kx^{k}W_{-k}\)

OMA-Vol. 6 (2022), Issue 2, pp. 1 – 28 Open Access Full-Text PDF
Yüksel Soykan, Erkan Taşdemir and Inci Okumuş

Abstract:In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}kx^{k}W_{k}\) and \(\sum\limits_{k=1}^{n}kx^{k}W_{-k}\) for generalized Tetranacci numbers are presented. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, and other fourth-order recurrence sequences.

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Compatible maps of type \((\beta)\) in intuitionistic generalized fuzzy metric spaces

ODAM-Vol. 5 (2022), Issue 3, pp. 1 – 12 Open Access Full-Text PDF
R. Pandiselvi, M. Jeyaraman and A. Ramachandran

Abstract: This paper presents several fixed point theorems for intuitionistic generalized fuzzy metric spaces with an implicit relation. Specifically, we utilize compatible maps of type \((\beta)\) in intuitionistic generalized fuzzy metric spaces to derive our fixed point theorems. Our results not only extend but also generalize some fixed point theorems that were previously established in complete fuzzy metric spaces. This is achieved by introducing a novel technique, which enhances the applicability and scope of the existing fixed point theorems.

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Generalizations of generating functions for basic hypergeometric orthogonal polynomials

OMS-Vol. 6 (2022), Issue 1, pp. 248 – 261 Open Access Full-Text PDF
Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang and Tanay V. Wakhare

Abstract: We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.

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Ultrasound guided anterior approach coeliac plexus ethanol neurolysis for pain relief in gastric and pancreatic malignancy

TCMS-Vol. 2 (2022), Issue 3, pp. 18 – 23 Open Access Full-Text PDF
D. Ashok Kumar, Ganesh Annamalai, Nadar Kalaivani Venkatasami and Sivabalan R G

Abstract: Background and Aim: Chronic cancer pain is one of the major challenges of palliative care and it is prevalent in 80\% of all the gastric and pancreatic malignancies. Adequate pain relief not only improves the drug compliance, but also alleviates depression among the cancer patients, thereby improving the quality of life. This study was carried out with the aim of evaluating the role of Coeliac Plexus ethanol Neurolysis (CPN) in pain relief among patients with gastric and pancreatic malignancy.
Methods and materials: This is an uncontrolled before-and-after non randomized trial. This bedside procedure was done in an ICU in chronic pain management centre. Trial coeliac plexus block was done after identification of coeliac trunk using ultrasound and 15 cc of 1% xylocard was given. After 30 minutes, pain relief was assessed with Numerical Rating Scale for pain (NRS). Patient was then given 20ml of 60% ethanol. Pain relief was documented using NRS immediately at 24hours, 72 hours,1 week and 3 months. Statistical analysis was done using Statistical Package for the Social Sciences version (SPSS) version 16.0. Paired t test was used to analyze the difference between variables.
Results: Our study shows statistically significant difference between pre-NRS and post immediate-NRS (mean 8.26\(\pm\)0.52 and 3.40 \(\pm\)0.47)(P value \(<0.0001\)) and significant decrease in NRS seen after 24 hours,72 hours,1 week and 3 months.
Conclusion: USG guided anterior approach coeliac plexus ethanol neurolysis is effective in decreasing pain associated with gastric and pancreatic malignancy.

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BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC