

Latest
Issue
Volume
14, No.
3,
September 2021
Articles 


Patterns of
Time Scale
Dynamic
Inequalities
Settled by
Kantorovich's
Ratio
In this
research
article, we
present an
interesting
generalization
of dynamic
Kantorovich’s
inequality
and
investigate
the additive
versions of
some dynamic
inequalities
on time
scales. The
time scale
dynamic
inequalities
extend and
unify some
continuous
inequalities
and their
corresponding
discrete
versions. 

Muhammad Jibril Shahab Sahir
JJMS,
2021, 14(3),
397410

In
this
paper,
we
introduce
the
notion
of
(s,
p)convex
functions
and
establish
an
integral
equality
and
some
HermiteHadamard
type
integral
inequalities
of
(s,
p)convex
functions
in
fractional
form.
Also
give
some
HermiteHadamard
type
integral
inequalities
of
product
of
two
(s,
p)convex
functions
in
fractional
form.


N. Mehreen
M. Anwar
JJMS,
2021, 14(3),
411435



Saadia
Benchabane
Smaïl
Djebali
JJMS,
2021, 14(3),
437452

Solving the Optimal Control of VolterraFredholm integrodifferential equation via Müntz polynomials
The main goal of the current paper is to present a direct numerical method for solving optimal control problem for systems governed by VolterraFredholm integrodifferential equation. This method is based upon a new form of orthogonal MüntzLegendre polynomials, and collocation method to transform the optimal control problem to a nonlinear programming problem with finitedimensional.
The accuracy and efficiency of the proposed method are examined with illustrative examples.


Neda
Negarchi
Sayyed
Yaghoub
Zolfegharifar
JJMS,
2021, 14(3),
453466



Ala’a AlKateeb
JJMS,
2021, 14(3),
467481

The Connected Restrained Edge Monophonic Number of a Graph
For a connected graph G = (V, E) of order at least two, a connected restrained edge monophonic set of a graph G is a restrained edge monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained edge monophonic set of G is the connected restrained edge monophonic number of G and is denoted by em_{cr}(G). We determine bounds for it and some general properties satisfied by this parameter are studied. For every pair a, b of positive integers with 4 ≤ a ≤ b, there is a connected graph G such that em_{r}(G) = a and em_{cr}(G) = b, where em_{r}(G) is the restrained edge monophonic number of G. Also, if n, d and k are positive integers such that 4 ≤ d ≤ n − 2, k ≥ 4 and n − d − k + 2 ≥ 0, then there exists a connected graph G of order n, monophonic diameter d and em_{cr}(G) = k.


A. P.
Santhakumaran
T. Venkata
Raghu
K.
Ganesamoorthy
JJMS,
2021, 14(3),
483492

On Nearly
Compact
Spaces via
PreOpen
Sets
Recently,
the first
author of
this paper
in a
collaborative
research
work
redefined
the concept
of nearly
compact
spaces by
preopen
sets and
obtained
some new
properties
on nearly
compact
spaces when
they are
studied from
this new
perspective.
In this
paper, we
continue to
study the
idea of near
compactness
via preopen
sets and
obtain some
new
characterizations
on nearly
compact
spaces.


Ajoy
Mukharjee
Pratap Kumar
Saha
JJMS,
2021, 14(3),
493503

On Commuting
Graphs
Associated
to
BCIAlgebras
In this
paper,
first, the
graph Γ(X)
associated
to a BCIalgebra
X is studied
and some
related
properties
are
established.
Especially,
a necessary
and
sufficient
condition
for Γ(X) to
be a
complete
graph is
given. After
that, the
commuting
graph
associated
to a BCIalgebra
X, denoted
by G(X), is
defined and
some related
properties
are
investigated.
The paper
provides a
necessary
and
sufficient
condition
for the psemisimple
part of X to
be an ideal.
Moreover, a
condition
for an
element of a
BCIalgebra
X to be
minimal is
given.
Finally, it
is proved
that a BCIalgebra
X is psemisimple
if and only
if G(X) is a
complete
graph. 

H. Harizavi
JJMS,
2021, 14(3),
505516

The
ThetaComplete
Graph Ramsey
Number
R(θ_{n},
K_{7});
n = 7; n ≥
14.
The Ramsey
theory is an
important
branch in
graph
Theory.
Finding the
Ramsey
number is an
important
topic in the
Ramsey
theory. The
Ramsey
number R(G,
H) is the
smallest
positive
integer n
such that
any graph of
order n
contains the
graph G or
its
complement
contains the
graph H. In
this paper,
we prove
that R(θ_{n},
K_{7})
= 6(n − 1) +
1, n = 7; n
≥ 14, where
θn is a
theta graph
of order n
and K7 is
the complete
graph of
order 7.


A.
Baniabedalruhman
JJMS,
2021, 14(3),
517526

Pompeiu Type
Inequalities
using
Conformable
Fractional
Calculus and
its
Applications
We establish
Pompeiu’s
mean value
theorem for
αfractional
differentiable
mappings.
Then, some
Pompeiu type
inequalities
including
conformable
fractional
integrals
are
obtained,
and the
weighted
versions of
this Pompeiu
type in
equalities
are
presented.
Finally,
some
applications
for
quadrature
rules and
special
means are
given. 

Samet Erden
M. Zeki
Sarikaya
JJMS,
2021, 14(3),
527544

Sum
2Irreducible
Submodules
of a Module
Let R be a
commutative
ring with
identity and
M be an
Rmodule. M
is said to
be
sumirreducible
precisely
when it is
nonzero and
cannot be
expressed as
the sum of
two proper
submodules
of itself.
In this
paper, we
will
introduce
the concept
of sum
2irreducible
submodules
of M as a
generalization
of sum
irreducible
submodules
of M and
investigate
some basic
properties
of this
class of
modules. 

F.
Farshadifar
H.
AnsariToroghy
JJMS,
2021, 14(3),
545554

CAS Wavelets
Stochastic
Operational
Matrix of
Integration
and its
Application
for Solving
Stochastic
ItôVolterra
Integral
Equations
This article
provides an
effective
technique
for solving
stochastic
ItôVolterra
integral
equations
using Cosine
and Sine (CAS)
wavelets. A
novel
stochastic
operational
matrix of
integration
of CAS
wavelets is
developed in
this article
for solving
stochastic
ItôVolterra
integral
equations.
Stochastic
ItôVolterra
integral
equation can
be reduced
to a system
of algebraic
equations
using the
newly
generated
stochastic
operational
matrix of
integration
of CAS
wavelets
along with
the
operational
matrix of
integration
of CAS
wavelets.
These system
of algebraic
equations
can be
solved using
appropriate
methods.
Convergence
and the
error
analysis of
the proposed
technique is
studied in
detail.
Numerical
examples are
presented in
order to
show the
efficiency
and
reliability
of the
proposed
method. 

S. C.
Shiralashetti
Lata Lamani
JJMS,
2021, 14(3),
555580







