Earthline Journal of Mathematical Sciences

Generalized Tribonacci Polynomials

2023-05-10T17:03:51+00:00

In this paper, we investigate the generalized Tribonacci polynomials and we deal with, in detail, two special cases which we call them (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials. We also introduce and investigate a new sequence and its two special cases namely the generalized co-Tribonacci, (r,s,t)-co-Tribonacci and (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices related to these polynomials. Furthermore, we evaluate the infinite sums of special cases of (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials.

On Inequalities for the Ratio of v-Gamma and v-Polygamma Functions

2023-05-20T17:47:12+00:00

In this paper, the author presents some double inequalities involving a ratio of v-Gamma and v-polygamma functions. The approach makes use of the log-convexity property of v-Gamma function and the monotonicity property of v-polygamma function. Some of the results also give generalizations and extensions of some previous results.

Some Computational Methods for Solving Extended General Bivariational Inclusions

2023-05-30T14:43:14+00:00

Some new classes of extended general bivariational inclusions are introduced and analyzed. It is established that the extended general bivariational inclusions are equivalent to the fixed point problems. This equivalence is used to discuss the existence of a solution of the extended general bivariational inequalities. Some new iterative methods for solving bivariational inclusions and related optimization problems are proposed. Convergence analysis of these methods is investigated under suitable conditions. Some special cases are also discussed of the main results as applications of the main results.

Single Acceptance Sampling Plan Based on Truncated Life Tests for Zubair-Exponential Distribution

2023-06-01T17:36:04+00:00

In this paper, a single acceptance sampling plan based on a truncated life test is proposed for a lifetime that follows the Zubair-Exponential (ZE) distribution. For some acceptance numbers, confidence levels, values of the ratio of the fixed experiment time to the particular mean lifetime, and the minimum sample sizes required to assert the specified mean life are obtained. The operating characteristic function values of the proposed sampling plans, consumer's and the producer's risk are presented. Other useful tables are presented and the results are discussed.